# Special theory of relativity  (Page 8/9)

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$x\prime =\gamma \left(x-vt\right)$

Lorentz factor appears in most of the relativistic equations including the calculation of relativistic effects like time dilation, length contraction, mass etc. An understanding of the beahviour of this factor at different relative velocity is intuitive for assessing the extent of relativistic effect. Few values of Lorentz factor are tabulated here.

Lorentz factors
Speed (v) 0 0.1c 0.2c 0.3c 0.4c 0.5c 0.6c 0.7c 0.8c 0.9c 0.99c 0.999c
Lorentz factor (γ) 1.000 1.005 1.021 1.048 1.091 1.115 1.250 1.400 1.667 2.294 7.089 22.366

Lorentz factor begins at 1 and as v->c, y->infinity. It is either equal to 1 or greater than 1. In other words, it is never less than 1. A plot of Lorentz factor .vs. relative speed is shown here.

## Space-time interpretation

We identify an event with spatial (x,y,z) and temporal (t) coordinates. Important point is that an event does not belong to any reference. It is described by different coordinates in different reference system. In classical description, spatial and temporal parameters are essentially independent of each other. The time t of an event can not be dependent on spatial specification (x,y,z,). Now, this independence is not there in relativistic kinematics. In order to imbibe the nature of space time relation, we shall work with few Lorentz transformations here.

We interpret an event in two inertial references which are moving with respect to each other at a velocity say 0.3c in x-direction. We shall consider very small time interval like 0.000005 second so that distance involved is easy to visualize. For convenience, we consider the approximate value of speed of light 300000000 m/s. In time 0.000005 s, the separation of two reference frame at the speed 0.3c works out to be 0.3 X 300000000 X 0.000005 = 450 m.

Here, we calculate both Galilean and Lorentz distance and time of events in two references for events identified in first reference by x and t values. Unprimed values refer to stationary reference, whereas primed values refer to moving reference which is moving right in x-direction with a relative velocity 0.3c. The calculations have been done using Excel worksheet (Reader can also try and verify the results) where distance is in meters and time in seconds.

Lorentz factors
x t x’(Galilean) t’(Galilean) x’(Lorentz) t’(Lorentz)
0 0 0 0 0 0
2 0.000005 -448 0.000005 -469.6317 0.0000052393
100 0.000005 -350 0.000005 -366.8998 0.0000051366

Since the origins of two references coincide for both Galilean and Lorentz transformations at t= t’=0, the space and time values are all zero as shown in the first row of the table.

Let us now consider the second row of the table. Here, position of event is x=2 m at time, t = 0.000005 s. In this time, primed reference has moved 450 m. According to Galilean transform, the event takes place at -450+2 = -448 m (to the left of origin) in the moving reference. Since time is invariant in Galilean transformation, the time of event is same in moving reference for non-relativistic Galilean transformation. However, when we employ relativistic Lorentz transformation, the event occurs at -469.6317 m (to the left of origin) in the moving reference. Here, the measurement of distance in moving reference is different than that calculated with Galilean transformation. Also, time is not invariant. The event occurs at 0.0000052393 s in this reference instead of 0.000005 s in the unprimed stationary reference. Thus, we see that both space and time are not invariant in Lorentz transformation.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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